Question

The two rods shown in figure have identical geometrical dimensions. They are in contact with two heat baths at temperatures ${100}^{\circ }C$ and $0^{\circ }C$. The temperature of the junction is ${70}^{\circ }C$. Find the temperature of the junction if the ods are interchanged.

Answer 1

Now, $\frac{Q}{t}$ remains same in both cases

In case I $\frac{K_A\times A\times (100-70)}{l}$

= $\frac{K_B\times A\times (70-0)}{l}$

$\Rightarrow 30K_A=70K_B$

In case II, $\frac{K_B\times \times (100-\theta )}{l}$

= $\frac{K_A\times A\times (\theta -0)}{l}$

$\Rightarrow 100K_B-K_B\theta =K_A\theta$

$\Rightarrow 100K_B-K_B\theta =\frac{70}{30}{K}_B\times \theta$

$\Rightarrow 100=\frac{7}{3}\theta +\theta$

$\Rightarrow 100=\frac{10}{3}\theta$

$\Rightarrow \theta =\frac{300}{10}={30}^{\circ }C$